This invention relates generally to game equipment, such as board game and video game equipment.
Game equipment of all types and kinds exist which simulate various real life situations. For example, game equipment which simulate sporting events, such as baseball, football and basketball, business endeavors, such as real estate, career advancement and the stock market, and socio-political events, such as war, are all known.
To the applicant's knowledge, although one game was found which refers to pyramid money schemes in its game terminology, neither that game nor any other utilizes in any dynamic way the mechanisms of "pyramids" herein applied for. Such pyramid schemes, also sometimes referred to as "ponzi" schemes, generally comprise a program which utilizes a pyramid or chain process, i.e., a process which utilizes a geometric progression, by which a participant in the program gives valuable consideration, usually a sum of money, for the opportunity or right to receive compensation in return for inducing other persons to become participants for the purpose of gaining new participants in the program. Each participant moves up through the pyramid, having paid an initial sum of money either to one person at the top of the pyramid or in portions to several persons at different levels above the first level. As the participant moves up, he/she either receives progressively larger payoffs or one large payoff if and when he/she reaches the top of the pyramid. The number of levels varies with different forms of pyramid programs. Although legislation has been enacted in several states which made the promotion of such schemes illegal, they still proliferate in the form, for example, of chain letters and empty security investments where the only positive cash flow results from the constant and essential recruitment of new investors. Some forms of pyramid schemes have been allowed to exist legally because a product is sold apart from the game itself, usually for less than $100.00.
A form of pyramid scheme which has recently come into vogue is called "The Airplane Game." In this version of the pyramid scheme, a player makes only one payment, to the person at the top of the pyramid. Using the jargon of the participants in the Airplane Game, the basic scheme works as follows: at a top a pyramid (or "airplane") is the Pilot; two Co-Pilots are on the second level of the pyramid or airplane; on the third level are four Crew Members; and on the fourth level are eight Passengers. The game actually originates when someone decides to be a Pilot and succeeds in recruiting two Co-Pilots who in turn recruit four Crew Members, and so on. The first pilot may make the most money on one round on one airplane because he or she may be paid not only by the Passengers but also the Crew and Co-Pilots; but that Pilot is also at greatest risk legally for starting the game in the first place. For most people, however, the game starts at the Passenger level. When eight Passengers have been recruited for the airplane by the Pilot, Co-Pilots and/or Crew Members, with each Passenger paying a sum of money to the Pilot, the Pilot "pilots out" of the program. The airplane then "splits" into two airplanes and each Co-Pilot "moves up" and becomes a Pilot of his own airplane. The four Crew Members separate into two pairs, each pair "moving up" to become Co-Pilots of a respective one of the two new airplanes. The eight Passengers who have just paid their money separate into two groups of four, each group "moving up" to become Crew Members of a respective one of the two new airplanes. At this point, everybody on board both of the airplanes begins recruiting eight new Passengers for each airplane.
If the game is infinite, there is no problem. In fact, a reasonable theoretical case might be made for the game proceeding indefinitely if it were brought in line with population growth rates and perhaps with the posting of a more realistic appraisal of the rate of return odds similar to legalized casino and racetrack gambling. [A pyramid scheme in fact, is not "gambling" per se, in that participants do not wager on an event outside their control with multiple outomes. Using a horse race analogy, a player in a pyramid scheme is wagering on a "horse" that the player is himself riding. In a general sense, the "gamble" is whether one can get in and out not only before the "bottoming out" comes, but also before one's friends get stuck as well.] The pace generally required for the Airplane Game to sustain interest and momentum, together with the necessity for recruitment, probably pushes the game to an early saturation point wherein the networks of participants so overlap that the supply of new and willing participants within a given time period and limited geographic area is essentially exhausted. Therefore legislation has been enacted making most of these pyramid games illegal, and police departments tend to shorten the effective game-playing time period by breaking up meetings when the numbers get too big.
An intense debate ensued in some circles as to whether this was a finite or infinite game, whether the game could work constructively if allowed to develop and evolve on its own without interference, and whether the game could be effectively assimilated into the already existing body of institutionalized pyramid variants, such as in the stock market, in political campaigns and elections, in tax structures and the federal budget. Those who believed in "the game" and those who did not, often became polarized. Aside from the issues of legality and mathematics, what may be most needed that is lacking in this and other pyramid schemes is the funding, promoting, and sponsoring of something of greater intrinsic value to the participants than the money they "invest." Some of the preferred embodiments of the game invention presented below take into account all of the above considerations.
Although from a legal point of view participation in actual pyramid of Ponzi schemes may not be advisable, the mechanism by which one "moves up" through a pyramid in accordance with a process which utilizes a geometric progressions is rather fascinating, and participating in the process in some benign way could be educational for children and adults especially those who might have difficulty visualizing a geometric progression when only tempted with an attractive piece of it.
It would be desirable therefore, to provide game equipment that in its play simulates the mechanism by which a participant "moves up" through a pyramid, and additionally to provide game equipment which simulates the dynamic interplay of population size and limited time-space events, wherein competition and/or cooperation interact with opportunities for growth or expansion, laws of diminishing returns, and saturation points.
Various games exist which incorporate the shape of a triangle or pyramid on the board without using a geometric progression. Some of these games refer to Pharoahs and Egyptian pyramids using a maze or labyrinth gameboard path. Other games have boards with space units laid out in arithmetic progressions (FIG. 1) which do not afford a repeated "split" into two new pyramids as do geometric progressions. Webster's New World Dictionary defines geometric progression as "a sequence of terms in which the ratio of each term to the preceding one is the same throughout the sequence." An example would be 2, 4, 8, 16, etc. An arithmetic progression is defined as "a sequence of terms each of which, after the first, is derived by adding to the preceding one a constant quantity." An example would be 1, 2, 3, etc.
Game boards do exist whereupon space units are arranged in geometric progressions, and the filling up of one row before moving up to the next row is a requirement of play. The number of space units filled by each player is usually determined by a chance device such as dice or a spinner, or by instructional cards. However, in all of the games searched by this applicant, only the player's own game piece moved up the pyramid. The filling of other space units was only implied, and the player game piece moved up the pyramid usually in a serial manner.
A variation of this was found in which all the spaces are covered by money chips and the player advances his game piece by spinning his color, removing arbitrarily or in sequence the money chips on one space in a given row and placing his game piece there, continuing in like fashion until all spaces of his color are exposed on that row, then advancing the game piece to the next row. (Copyright Registration No. VA 19-856). One could argue that this represents the pyramid money scheme if one imagines that each time the game piece moves and the player collects money chips, he/she is collecting the payoffs which, when all are collected from a given row means that row is filled and this advances the player to the next higher row, there to collect more payoffs, and so on. If one imagines even further, the money chips in each row therefore represent money from a new player filling a space on the bottom row and paying that portion upward in order to fulfill the "payoff" requirements that may get progressively larger as one moves up the pyramid simply because there are fewer recipients of the portion earmarked for each higher row, even if that portion is the same.
Again however, the only game pieces that actually move up are the individual game pieces of the respective players. The rest of the pyramid process in terms of actual movement, is at best implied.
Another "pyramid" game was found (copyright Registration No. VA 71-489) which actually refers to pyramid money schemes in its play. The game board is arranged, not in a triangular pyramid shape as such, but in rows of equal length subdivided into space units in size progressively larger and number progressively fewer from the bottom up to a top row of one. The sequence of rows is a geometric progression 2n with 32 units in the bottom row and subsequent rows of 16, 8, 4, 2, and 1, with an extra top row of 1 for a total of 64 units throughout.
Player game pieces are advanced in turn by a roll of the dice and according to instructions of cards when a player lands of a space unit that is red or green. "Recruitment" of additional players and "split" of the pyramid are some of the instructions on the cards, which in the former case advance the player serially, and in the latter case advance the player up to the first space on the next higher row no matter what his position and no matter whether a row has been filled. Afterwards, movment resumes in serial fashion by roll of the dice. Green cards generally move the player game piece forward and up, red cards move the player game piece backward and down. Nevertheless, such "recruitment" and "splitting" are only implied and arbitrarily so, by drawing a given card. No actual game pieces are recruited onto the board; only the player game pieces move. The actual movement up the pyramid is serial and does not effect a change according to a geometric progression even though the space units are laid out in that manner. There is no room for splitting because there is only one pyramid. Furthermore, more than one player game piece may occupy the same space unit, so that what happens to one game piece does not affect the other except by one getting to the top first and thereby winning. There is also no actual collecting or exchanging of play money in the game. (The use or non-use of play money or chips is not the focus of this application, unless it bears directly on the pyramid scheme process and its geometric progression.)
It may be concluded that in each of the above games the relationship of the game apparatus to a pyramid scheme and/or geometric progression is a static relationship rather than a dynamic one.